Arrival first queueing networks with applications in kanban production systems

In this paper we introduce a new class of queueing networks called {\it arrival first networks}. We characterise its transition rates and derive the relationship between arrival rules, linear partial balance equations, and product form stationary distributions. This model is motivated by production systems operating under a kanban protocol. In contrast with the conventional {\em departure first networks}, where a transition is initiated by service completion of items at the originating nodes that are subsequently routed to the destination nodes (push system), in an arrival first network a transition is initiated by the destination nodes of the items and subsequently those items are processed at and removed from the originating nodes (pull system). These are similar to the push and pull systems in manufacturing systems

Zero-automatic queues and product form

We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable 0-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of 0-automatic queues, we recover the simple M/M/1 queue, and Gelenbe's G-queue with positive and negative customers

Technical Report: Analytical Modeling and Throughput Computation of Blockchain Sharding

Sharding has shown great potential to scale out blockchains. It divides nodes into smaller groups which allow for partial transaction processing, relaying and storage. Hence, instead of running one blockchain, we will run multiple blockchains in parallel, and call each one a shard. Sharding can be applied to address shortcomings due to compulsory duplication of three resources in blockchains, i.e., computation, communication and storage. The most pressing issue in blockchains today is throughput. Hence, usually the main focus is to shard computation which leads to concurrent transaction processing. In this report, we propose new queueing-theoretic models to derive the maximum throughput of sharded blockchains. We consider two cases, a fully sharded blockchain and a computation sharding. In the former nodes are exclusive to each shard in terms of their responsibilities, i.e., block production, relaying and storage. In the latter though, only block production is exclusive and nodes relay and store every piece of information. We model each with a queueing network that exploits signals to account for block production as well as multi-destination cross-shard transactions. We make sure quasi-reversibility for every queue in our models is satisfied so that they fall into the category of product-form queueing networks. We then obtain a closed-form solution for the maximum stable throughput of these systems with respect to block size, block rate, number of destinations in transactions and the number of shards. Comparing the results obtained from the two introduced sharding systems, we conclude that the extent of sharding in different domains plays a significant role in scalability

Datacenter Traffic Control: Understanding Techniques and Trade-offs

Datacenters provide cost-effective and flexible access to scalable compute and storage resources necessary for today's cloud computing needs. A typical datacenter is made up of thousands of servers connected with a large network and usually managed by one operator. To provide quality access to the variety of applications and services hosted on datacenters and maximize performance, it deems necessary to use datacenter networks effectively and efficiently. Datacenter traffic is often a mix of several classes with different priorities and requirements. This includes user-generated interactive traffic, traffic with deadlines, and long-running traffic. To this end, custom transport protocols and traffic management techniques have been developed to improve datacenter network performance. In this tutorial paper, we review the general architecture of datacenter networks, various topologies proposed for them, their traffic properties, general traffic control challenges in datacenters and general traffic control objectives. The purpose of this paper is to bring out the important characteristics of traffic control in datacenters and not to survey all existing solutions (as it is virtually impossible due to massive body of existing research). We hope to provide readers with a wide range of options and factors while considering a variety of traffic control mechanisms. We discuss various characteristics of datacenter traffic control including management schemes, transmission control, traffic shaping, prioritization, load balancing, multipathing, and traffic scheduling. Next, we point to several open challenges as well as new and interesting networking paradigms. At the end of this paper, we briefly review inter-datacenter networks that connect geographically dispersed datacenters which have been receiving increasing attention recently and pose interesting and novel research problems.Comment: Accepted for Publication in IEEE Communications Surveys and Tutorial